Sleeves are often used to drive screws and are usually made of materials harder than those used to manufacture screws. When a sleeve is used to drive a screw, the size of the sleeve is usually larger than that of the screw nut to enable easy engagement of the sleeve with the screw nut, thereby leaving space between the sleeve and the screw nut. During operations, the space may cause the sleeve to slip and the driving force may be applied at the corners of the screw nut, thereby deteriorating the corners and making the screw difficult to drive. Sleeves that can be used to drive a screw with a damaged nut have been discussed in US20080245195, US20060117917 and US20070125204. However, the sleeves provided by US20060117917 and US20070125204 can only drive a screw in a single direction and cannot work effectively, because they can only grip the screw at two positions on each side of the screw nut and thus cannot apply the driving force properly. Therefore, there remains a need for a new and improved sleeve to overcome the problems stated above.